How to create a binary search tree from an array
I’m going to discuss how to create a binary search tree from an array. This will be a basic integer array that contains 6 values that are unsorted.
Let’s begin by first establishing some rules for Binary Search Trees (BST):
1. A parent node has, at most, 2 child nodes.
2. The left child node is always less than the parent node.
3. The right child node is always greater than or equal to the parent node.
The first value in the array is 7, so the first step in constructing the tree will be to make 7 the root node, as shown here:
With the root node set, all of the remaining values will be children of this node. Referencing our rules from the beginning of this post we know the child nodes will be designated as the right or left child nodes depending on their value. Therefore the first step we’ll take for adding the 2 to the tree will be to compare it to the root node:
If the 2 is less than the 7, it will become the left child node. If the 2 is greater than or equal to 7 it will move to the right. Since we know that the 2 is less than 7 we designate it as the left child node, as shown here.
Following the same pattern, we perform the same comparison with the 9 value in the array. Comparing the value of 9 to the root node of 7 we know that 9 is the right child.
Making our way through the array we come to the 1. We’ll start with comparing the array to 7, which it’s less than. So we move to the left and compare it with 2, it’s less than 2 and 2 doesn’t have any children to the left, so we make 1 the left child of 2.
Continue making our way through the array we come to the 5. We’ll start with comparing the array to 7, which it’s less than. So we move to the left and compare it with 2, it’s greater than 2 and 2 doesn’t have any children to the right, so we make 5 the right child of 2.
Lastly we will insert the value 14. We’ll start with comparing the array to 7, which it’s greater than. So we move to the right and compare it with 9, it’s greater than 9 and 9 doesn’t have any children to the right, so we make 14 the right child of 9.
We are done creating our Binary Search Tree (BST). Binary search trees are typically only efficient if they are balanced. A balanced tree is a tree where the difference between the heights of sub-trees of any node in the tree is not greater than one. An example of this is a AVL tree.
An AVL Tree is a self balancing binary search tree (BST). It is named after Adelson-Velskii and Landis, the inventors…
You can watch a playlist on Binary Search Trees here, or watch the playlist below:
If you are also interested in reading up a little bit more on Binary Search Trees and other data structures & algorithms, then I strongly recommend you check out the amazing book Introduction to Algorithms, 3rd Edition (The MIT Press) 3rd Edition. This book goes over topics like binary search trees, sorting algorithms, heap sort, hash tables, red and black trees, divide and conquer algorithms, greedy algorithms and the list goes on !
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